In roofing installations, membranes are laid on top of substrates such as roofs. The membranes are secured over the substrates by membrane plates set down over the membranes. A fastener passes through the membrane plates, is driven through the membranes, and is driven into the substrates below for securing the membrane plates on the membranes. The membrane plates are also referred to as stress plates or clamping plates, and are commonly made of metal. Sometimes, small protrusions project downwardly from the membrane plates for direct contact with the membranes underneath. And in some installations, insulation is inserted between the membranes and substrates.